Assume that x and y are both differentiable functions of t and are related by the equation y = cos(4x). ㅠ dx dy Find when x = given dt -3 when x = 3 dt == 100 ㅠ

Q: 36. Which one of the following is true for all z ER? (a) z sin(2) dx = (1-2) cos(x) + C (c) (b)…

A: Now that we know that the integral of x sin x is equal to −x cos x + sin x + C, we will derive this…

Q: Find the volume and the dimensions of the largest rectangular box in the first octant with three f…

A:

Q: Given the following piecewise function, evaluate lim f(x). x→2 -x² - 2x - 2x² - 1 f(x) = -2x² - 3x +…

A: Explanation of the answer is as follows

Q: Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 8x² +17x - 10 on the interval…

A:

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

A:

Q: If we let u = cos t, then the integral [(sint). In (cost) dt can be expressed as - [In(u) du 0…

A: An integral is given. We have to write the substitution form of the integration in terms of the…

Q: Evaluate the indefinite integral Го уз (y² - 3) dy. y5 - 3y³ + C О О yo 3y1 +C 6 4 O y1 / y³ 1 (4 -…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2 Σ(-1)+1n? + 5 m2 + 4 n=1

A:

Q: Q3/ Evaluate: ff(x+y) dy dx for the region bounded by the x = 0, x = 2, y = x and y = x + 2

A:

Q: If w = cos(xyz), compute for O-x²yz cos(xyz) - x sin(xyz) -x²yz cos(xyz) + x sin(xyz) O x²yz…

A: This question can be solved using the concept of partial derivatives.

Q: A tank contains 420 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram…

A:

Q: Q3/ Evaluate: ff(x+y) dy dx for the region bounded by the x=0, x=2, y = x and y = x + 2

A:

Q: 1) Compute the value of representation √√√√3-i in exponential representation and polar

A:

Q: If f(x) = 6 sin¯¹(x²), find ƒ'(x). Find ƒ'(0.5).

A: This question is related to differentiation, We will solve it using given using given information.

Q: Evaluate the definite integral. TT/3 [C [(sec t tan t)i + (tan t)j + (2 sin t cos t)k] dt 10

A:

Q: Consider a function f that is continuous on [-2, 4] with f'(x) = 0 whenever x = 3 or x = 5. Suppose…

A:

Q: B/ Find the value of 1. tan+e O 1 2 dx 2. tante

A:

Q: Find the limit. Enter the exact answer. If the limit does not exist, indicate that using the check…

A:

Q: Consider the linear system of equations a) For which values of a does the linear system have no…

A:

Q: Solve the initial value problem y"+y=f(t), y(0)=y'(0) = 0, (21 2t if 0 1

A: Here is the solution of the given problem. We solve this problem by using Laplace transformation

Q: 1 1- x

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Solve the given initial-value problem. y x = 6y², x(8) = 1 dy x(y) = Give the largest interval I…

A: To solve the initial value problem.

Q: Q1: Sketch the signals A. x(t) x(-1/2) A CL x(2(1+2)) x(−1+1) Ates Ades 0 2 B. 2 x(t) 0 1 x (3t),…

A: Given data:- Part A=   Part B

Q: If we use IBP to evaluate Ixe xe²x dx, then the most suitable choice for u and dv are

A:

Q: 7. y = (x+1)* 9. y = Inlog, x

A:

Q: -7-6-5-4-3-2- 6 5 4 3 -2 -5. -6. H 1 2 3 4 5 6 7

A:

Q: The plane x + y + 2z = 12 intersects the paraboloid z = x² + y2 in an ellipse. Find the points on…

A: Suppose the point nearest to origin with the condition that it is not the ellipse that is obtained…

Q: State

A:

Q: Find the second derivative of the function. f(x) = 5(2 − 7x)ª

A: Given query is to find the second derivative.

Q: Given the piecewise function below, find the value of k which makes the function continuous. f(x) =…

A:

Q: 3. 2 cos¹ √x = cos ¹(2x-1) 0≤x≤1

A: We have to find out

Q: 4x Compute the values of dy and Ay for the function y = e + 2x given x = 0 and Ax = dx = 0.05. Round…

A: Follow the procedure given below.

Q: Q4/ 1- Evaluate: ffy sinx dy dx

A: According to company rule we can answer only first question and rest can be reposted.

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

A: Given problem:- Initially 100 milligrams of a radioactive substance was present. After 6 hours the…

Q: If sin t = and t is in quadrant I, find the exact value of sin (2 t), cos (2 t), and tan (2 t)…

A:

Q: Which point is not a solution to the equation 3x - 4y + z-12=0? a) (-8,-9,0) b) (4,1,4) c) (16,10,4)…

A: The point which donot satisfies the equation will not be a solution .

Q: dy Using logarithmic differentiation, find dx NOTE: Express your answer in terms of x only. dy dx =…

A:

Q: tan(2x) x+02sin²(x) Evaluate: lim O a. ∞ O b. -∞ O c.0 O d.-1

A: We have to evaluate limx→0- tan2x2sin2x         Here two sided limit does not exist.…

Q: Use the formula z = ['(t) x r²(c)]. r²(c), Ir'(t) x r"(t)1² r(t) = 9t, to find the torsion of the…

A:

Q: Use Simpson's Rule with n = 10 to estimate the arc length of the curve. (Round your answer to six…

A:

Q: x²-100 4. lim x-10 x+10

A:

Q: Find the derivative y = x tan^¹x − In √√1 + x²

A:

Q: Determine the domain of the function f(x, y) = 1 √x + y² O R² ○ {(x, y) | x > -y²} ○ {(x, y) | x ‡…

A: To find the domain of square root function , values of square root must be greater or equal to zero…

Q: Consider the following statements: I. 27x+3, 27x11, and 27x + 17 are antiderivatives of 27. II. In…

A: Given : 1. 27x+3, 27x-11 and 27x+17 are antiderivatives of 272. In general, 27x+C is an…

Q: If integration using u-substitution technique is used to solve for ∫2e2x1−e4x dx/square root of…

A:

Q: Let f(x) = { x - 2 7x 38 Find the following limits. lim f(x) = x→6- lim f(x) = = x→6+ lim f(x) = x-6…

A: This question can be solved using the concept of limits.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Here we have to check the convergence of given sequence

Q: Use the Laplace transform to solve the given initial-value problem. y'' − y' = et cos t,    y(0) =…

A:

Q: If f(t) = sin−¹(3t), find ƒ'(t). Use exact values. ƒ'(t) =

A:

Q: Given the following piecewise function, evaluate lim f(x). x 17 -2x² - 2x f(x) 3x - 2 x² + 3 = if if…

A: